Microscopic Theory of Entropic Bonding for Colloidal Crystal Prediction

TL;DR

This paper introduces a first principles statistical mechanics theory that predicts colloidal crystal structures formed by hard particles based on entropy, matching previous simulation results and advancing understanding of entropic self-assembly.

Contribution

The authors develop a novel theoretical framework that predicts colloidal crystal structures from particle shape using excluded volume calculations, without relying on simulations.

Findings

Accurately predicts structures for four families of hard polyhedra.

Matches previous simulation results in structure prediction.

Provides a chemical-bond-like description of entropic forces.

Abstract

Entropy alone can self-assemble hard particles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Although particle-based molecular simulation is a powerful tool for predicting self-assembly by exploring phase space, it is not yet possible to predict colloidal crystal structures a priori from particle shape as we can for atomic crystals based on electronic valency. Here we present such a first principles theory. By directly calculating and minimizing excluded volume within the framework of statistical mechanics, we describe the directional forces that emerge between hard shapes in familiar terms used to describe chemical bonds. Our theory predicts thermodynamically preferred structures for four families of hard polyhedra that match, in every instance, previous simulation results. The success of this first principles approach to entropic colloidal crystal structure prediction furthers fundamental understanding of both entropically driven crystallization and conceptual pictures of bonding in matter.